Is a coin with a 1935 Mercury head dime and a wheat penny back authentic?

You have what's known as a "Magician's Coin".

This is NOT something that was done at the Mint.

This was made by altering two normal coins and gluing the altered pieces back together. Use a magnifier to check just inside the rim on one side of the coin -- you are looking for the seam where the two pieces were joined -- it could be on either side of the coin.

This type of novelty item sells regularly in Magic Shops and on eBay.com for a couple dollars.

I ,

Dan Moore

The Working Man's Rare Coins

http:/www.workingmancoins.com

Since this piece was made from coins with designs that have been discontinued for many years, it would bring more than one made from coins currently found in circulation. However, since no one is "making a market" in these items, about the only way to determine how much it will bring is to put it up for auction. You might search eBay to see if anything similar has been offered lately.